Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #66016 | C2 | semidirect |
| 2. C5×#495 | C2 | semidirect |
| 3. #65478 | C2 | semidirect |
| 4. #65473 | C2 | semidirect |
| 5. #65460 | C2 | semidirect |
| 6. SD16×Dic5 | C2 | semidirect |
| 8. #65441 | C2 | semidirect |
| 9. #65344 | C2 | semidirect |
| 10. #64978 | C2 | semidirect |
| 11. #64969 | C2 | semidirect |
| 72. #495 | D5 | semidirect |
| 200. C5 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66016 | 2 |
| C5×#495 | 2 |
| #65478 | 2 |
| #65473 | 2 |
| #65460 | 2 |
| SD16×Dic5 | 2 |
| #65448 | 2 |
| #65441 | 2 |
| #65344 | 2 |
| #64978 | 2 |
| #64969 | 2 |
| #3173 | 5 |